Presidential Address 2012

Part of the 2012 MA Conference

What is the source?

Paul Andrews, Presidential Address, MA conference, Keele, 11 April 2012.

What's the big idea?

Learning from Others is at the core of pedagological improvement. There are some really important lessons we can learn from practitioners in other countries and some reasons why certain countries aren't necessarily as good role models as they might first appear.

What is their background?

The 100th President of the Mathematical Association. Dr Andrews has spent the last 20 years working in comparative mathematics education.

What are they saying?

Dr Andrews has kindly offered to share his slide presentation, but regrets that the video clips that accompanied it have been removed to comply with his research ethics code:

Why is learning from others important?
20 years ago I went to Budapest: I was very lucky. Hungarians are net exporters of good mathematicians. I went to see how they taught mathematics.

"When I was there I saw one of the best problems I've ever seen:

An isosceles triangle has 9 square units.

The triangle has been drawn with each vertex on an integer grid point.
One of the vertices is at the point (3,1).
How many different triangles satisfy these conditions?"

For the answer, reveal this comment or open this document: .

The pupils worked independently for a few minutes and then they discussed the reasons.

"For me it is the fact that the teacher knew this was a good problem that is interesting."

Investigating how others do things.

• Is interesting
• Offers new lenses for analysing my own classroom
• Challenges my assumptions
• Makes the stange familiar and the familiar strange
• Facilitates an evaluation of adaptive potential
• Helps me understand how culture impacts in hidden ways
• Allows a system to evaluate its effectiveness.

Faming today's talk
The current governemnt has made a big issue of listening to stake holders as preparation for curriculum reform

Is there a big proble with UK maths teaching?
Yes! I think there is and it's long lasting.
in the 1990's at teh height of the SMPs 5-16 scheme's popularity
Leung 1995: "They start with the teacher completing various administrative matters uincluding a register. Students could then work ontheir own while the yteacher circulated the room busily helping students withdifficulties and recording their latest booklet test marks. Finally, a few minutes before the bell, teachers would ask students to pack away."
Anyone want ticket 37 for 10 pence?
A student learning ratio. "Rat e o."

A post SMP Outsider's Perspective
English math privaliges pragmatism over theory
A spiral curriculum enables topics taught over a small numer of lessons to be introduced at an elementary level, icked up again later and taught in
recipe
proof is ratre
standard algorithms give low priority

The Typical English Textbook
short chapters fewer woeds
Little explanation some worked exmaples
little technical vocab
little

The Typical French Textbook
Activites small investigations, to introcuce a notion
L'essentiel compulsory part yo be taught and understod the cours
excercises graded

English Teachers' Beliefs About Mathematics
Applicable number basic skills
few talked about exploratory activity
Some

Hingarian Teachers' Beliefs
mathematical problem solving and the usefulness coming out of this

Another Hungarian Problem
0,45
The interest was in the way the teacher managed the whole class to participate in collective problem solving.

What and Where are there alternatives?

Does PISA Help us?
Authentic real-world tasks.
Boost average PISA scores by 25 points over the next 20 year implies an aggregate gain of OECD GDP of USD 115 trillion...

The Finnish PISA Phenomenon?
Always top ten, the

How do the Finns Explain Their Success 1
comprehensive with no independent sector attend local comprehensive
all taught mixed ability, not tracked, not streamed
lowest between school variation in PISA
integrated SEN about 1 in 6. Get provision in class, not extracted. Throw a lot of money at langauge acquisition and basic math skills
High public esteem
A 4 to 5 year masters is an essential pre-requisite, so teachers are trusted and respected.

Example lesson in Finnish teaching
Percentages taught to grade 5 class - it isn't stunning. Teachers constantly leave learners to infer whether suggestions are good or not. They neitehr seek nor offer clarification. So what on earth is going on.
Perspectives on Finnish Teaching
intelligence and emotional wasteland (Carlgren et al 2006)

Finnish PISA Success: at what cost?
Performance on TIMMS 1999 was average for European nations and masked disappointingly low scores on algebra (498) and geometry (494)
Finland used to be a Swedish colony and Swedish speakers dominate their economy, yet the Swedish speaking Finns underperform
Reading competence used to be a prerequisite for receiving Lutherian sacrements including marriage, so there is no illiterate underclass.
Their library system is very strong.

Flanders (Flemmish Belgium) outperforms Finland
Their performance was strong across all domains in TIMMS

Nominally comprehensive, dense population and multicultural
vocational, humanities and clasical education pathways - nominally choice, but actually pupils are guided
Video clip using manipulatives (Dienes blocks?) to demonstrate 2% of 900.
2% of 900 = 2 of every hundred for 900 = 2 on every hundred for 900 = ...

English teacher
start with 10% of ...

Looking for general principles
Some more video clips - solving equations in Finland, Flemmish Belgium and Hungary
The Hungarian problem was stated in context of sacks of potatoes. This allows the scale metaphor to become more concrete.

It's important to start with the explanation of the analytic approach when the unknown is on both sides. Otherwise you're struggling to force the pupils to apply a 'difficult' method to solve a simple linear equation for which it is excessive.

Where can I learn more?

If you have any suitable links to related texts, web sites or other sources, put them here.

What next?

Explain what relevance this has to us:

• How will this change your practice?
• What do you or we need to do differently to make use of this idea?
• How will it improve learning?

Pay particular attention to the last question: if you can't see how it improves learning, say so.